The L-class of non-Witt spaces

• Autores: Marcus Banagl
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 163, Nº 3, 2006, págs. 743-766
• Idioma: inglés
• DOI: 10.4007/annals.2006.163.743
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• Resumen

  • Characteristic classes for oriented pseudomanifolds can be defined using appropriate self-dual complexes of sheaves. On non-Witt spaces, self-dual complexes compatible to intersection homology are determined by choices of Lagrangian structures at the strata of odd codimension. We prove that the associated signature and L-classes are independent of the choice of Lagrangian structures, so that singular spaces with odd codimensional strata, such as e.g. certain compactifications of locally symmetric spaces, have well-defined L-classes, provided Lagrangian structures exist. We illustrate the general results with the example of the reductive Borel-Serre compactification of a Hilbert modular surface.